On The Problems About Covering Of Circles

Let C,D be plane convex polygons and let C1,C2,...be the homothetic copies of C.Wesay that the sequence {Cn} permits a covering of D if D D(?)Cn.In particular,a covering of a plane convex body D with a sequence of polygons {Pn} is parallel if there is a certain straight line of D such that each {Pi}has a side parallel to this line of D.In chapter 1 we look at the parallel covering of a quarter circle with a radius of 1 with any sequences of squares and get the following result:Any(finite or infinite)sequence of squares permits a parallel covering of a quarter circle D with radius 1 provided that the total area of the squares is not less than 2(?),In chapter 2 we consider the parallel covering of a unit circle with any sequences of squares and get the following results:Any(finite or infinite)sequence of squares permits a parallel covering of a semicircle B with radius 1 provided that the total area of the squares is not less than 4.Any(finite or infinite)sequence of squares permits a parallel covering of an arch A with bases of length 2h and height(?)provided that the total area of the squares in not less than 4h2.Any(finite or infinite)sequence of squares permits a parallel covering of a unit circle C provided that the total area of the squares is not less than 8.The smallest radius of n congruent closed circular discs that can cover an isosceles right triangle of unit leg length(including its interior)will be denoted by τn.In chapter 3 we consider the loosest circle coverings of an isosceles right triangle of unit leg length and get the following results:...